Units and Dimensions Questions and Answers

Answer: A

Terms that are added or equated must carry the same dimensions, which is the first check to make on any derived expression. An equation may be homogeneous and still be written in mixed units, which is a separate problem.

Answer: B

It can only prove an equation wrong, since a dimensionally consistent equation may still carry the wrong numerical coefficient. It remains the cheapest single check available. Running it before any arithmetic saves a great deal of time.

Answer: C

Reducing a derived unit to base units is how any conversion or consistency check is settled. The pascal follows from the newton divided by an area and the watt from the joule divided by time. Every derived unit reduces to the seven base ones.

Answer: D

Viscosity is a stress divided by a velocity gradient, and reducing that combination gives mass per length per time, the poise or pascal second. Kinematic viscosity divides this by density and is length squared per time instead.

Answer: A

Correct answer: 3 bar

Gauge pressure is measured from atmospheric, so \[ P_{abs} = P_{gauge} + P_{atm} = 2 + 1 = 3\ \mathrm{bar}. \] A gauge reading zero means the vessel is at atmospheric pressure, not at vacuum, and a negative gauge reading is a partial vacuum. The distinction is worth care because a plant gauge and a thermodynamic calculation use different zeros.

Answer: B

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the cause. \( PV = nRT \) is derived on the assumption that pressure falls to zero when the molecules are absent, so it requires a pressure measured from that true zero. Substituting a gauge reading understates the pressure by one atmosphere - a small error at 50 bar and a very large one at 2, which is where it usually bites.

Answer: C

The first two are correct because the scales differ only in their zero. The third confuses a temperature with a difference, and twenty degrees Celsius is about two hundred and ninety-three kelvin. Adding 273 converts a Celsius temperature to kelvin.

Answer: D

A temperature difference has the same magnitude in Celsius as in kelvin, so a sensible heat calculation may use either. The other three all divide by or exponentiate the temperature itself, which requires the absolute scale.

Answer: A

The reference must be stated because water itself changes density with temperature, and a value quoted without it is ambiguous. For gases the reference is air rather than water. Density itself carries units while specific gravity does not.

Answer: B

Correct answer: 800

Specific gravity is a ratio to the density of water, which is 1000 kg per cubic metre, so \[ 0.8 \times 1000 = 800\ \mathrm{kg/m^3}. \] It is dimensionless by construction, and the 0.8 offered is the specific gravity itself rather than a density - a substitution that would leave any subsequent calculation wrong by a factor of a thousand.